While planar shock waves are known to be stable to small perturbations in the sense that the perturbation amplitude decays over time, it has also been suggested that plane propagating shocks can develop singularities in some derivative of their geometry (Whitham (1974) Linear and nonlinear waves. Wiley, New York) in a nonlinear, wave reinforcement process. We present a spectral-based analysis of the equations of geometrical shock dynamics that predicts the time to singularity formation in the profile of an initially perturbed planar shock for general shock Mach number. We find that following an initially sinusoidal perturbation, the shock shape remains analytic only up to a finite, critical time that is a monotonically decreasing function of the initial perturbation amplitude. At the critical time, the shock profile ceases to be analytic, corresponding physically to the incipient formation of a “shock-shock” or triple point. We present results for gas-dynamic shocks and discuss the potential for extension to shock dynamics of fast MHD shocks.
W. Mostert et al., "Singularity Formation in the Geometry of Perturbed Shocks of General Mach Number," 31st International Symposium on Shock Waves 1, pp. 887-894, International Shock Wave Institute (ISWI), Jul 2017.
The definitive version is available at https://doi.org/10.1007/978-3-319-91020-8_106
31st International Symposium on Shock Waves, ISSW31 (2017: Jul. 9-14, Nagoya, Japan)
Mechanical and Aerospace Engineering
Article - Conference proceedings
© 2017 International Shock Wave Institute (ISWI), All rights reserved.
14 Jul 2017